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This document discusses linear equations in two variables. It begins by presenting the general form of a linear equation as ax + by + c = 0, where a, b, and c are real numbers. It then explains that a linear equation can have infinitely many solutions (x,y value pairs) that satisfy the equation, and these solutions lie on a straight line. The document provides an example of a single linear equation and shows its graph on the Cartesian plane. It also discusses systems of two linear equations, explaining that their solutions occur where the lines intersect. The document covers various algebraic methods for solving systems of linear equations, including elimination by substitution or equating coefficients, and solving by cross multiplication. It provides examples to illustrate these solution

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Pair of linear equation in two variable

This document discusses linear equations in two variables. It defines a linear equation as an equation between two variables that forms a straight line when graphed. It then defines a linear equation in two variables as an equation with two variables, usually x and y, where the variables are multiplied by a number or added to another term. The document goes on to explain that a system of linear equations can have one solution, no solution, or infinitely many solutions depending on whether the lines intersect at one point, do not intersect, or coincide. It describes algebraic and graphical methods for solving systems of linear equations, focusing on substitution, elimination, and cross-multiplication algebraic methods.

Maths ppt linear equations in two variables

AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.

Linear equations in 2 variables

This document discusses linear equations. It defines linear equations as algebraic equations with terms that are constants or the product of constants and variables. Linear equations can have one or more variables. The document describes variables, constants, and examples of linear equations with one and two variables. It explains how to graph and solve systems of linear equations using graphical and algebraic methods like elimination and cross multiplication. Graphical methods involve plotting the lines defined by each equation and finding their point(s) of intersection. Algebraic methods eliminate variables to solve for the remaining ones.

Pairs of linear equation in two variable by asim rajiv shandilya 10th a

This document provides an overview of pairs of linear equations in two variables. It discusses representing such equations graphically as two lines with possible solutions of unique intersection, no intersection, or overlapping lines. Algebraic methods for solving pairs of linear equations are presented, including substitution, elimination of a variable by making coefficients equal, and cross multiplication. Examples are provided to illustrate each method. The document also describes how to reduce equations not initially in the standard form for a pair of linear equations to that form so the equations can be solved using the described algebraic techniques.

LINEAR EQUATION IN TWO VARIABLES PPT

The document provides information about solving linear equations and systems of linear equations. It defines a linear equation as an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses three methods for solving a pair of linear equations:
1) The graphical method involves plotting the equations on a graph and finding their point of intersection.
2) The algebraic methods include substitution, elimination, and cross-multiplication. Substitution involves solving one equation for one variable and substituting it into the other equation. Elimination involves eliminating one variable to obtain an equation with just one variable.
3) Cross-

Quadratic equations class 10

The document discusses quadratic equations. It defines the standard form of a quadratic equation as ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The values of x that satisfy the equation are called the roots. A quadratic equation can have two distinct real roots, two equal real roots, or no real roots depending on the discriminant. The quadratic formula x = (-b ± √(b2 - 4ac))/2a is presented to directly obtain the roots from the standard form. The discriminant (D = b2 - 4ac) determines the nature of the roots. If D > 0, there are two distinct real roots. If D = 0,

Pair of linear equations in two variables for classX

This document discusses methods for solving pairs of linear equations in two variables: substitution, elimination, and cross-multiplication. The substitution method involves solving one equation for one variable and substituting it into the other equation. The elimination method involves multiplying the equations by constants to make coefficients equal and then adding or subtracting the equations to eliminate one variable. The cross-multiplication method involves cross-multiplying the coefficients of the equations to derive an equation with one variable that can then be solved.

Linear equation in two variable

The document discusses methods for solving systems of linear equations in two variables:
1) Graphical method involves plotting the lines defined by each equation on a graph and finding their point of intersection.
2) Algebraic methods include substitution, elimination by equating coefficients, and cross-multiplication. Elimination involves manipulating the equations to eliminate one variable and solve for the other.
3) Examples demonstrate solving a system using substitution and elimination to find the solution values for x and y.

Pair of linear equation in two variable

This document discusses linear equations in two variables. It defines a linear equation as an equation between two variables that forms a straight line when graphed. It then defines a linear equation in two variables as an equation with two variables, usually x and y, where the variables are multiplied by a number or added to another term. The document goes on to explain that a system of linear equations can have one solution, no solution, or infinitely many solutions depending on whether the lines intersect at one point, do not intersect, or coincide. It describes algebraic and graphical methods for solving systems of linear equations, focusing on substitution, elimination, and cross-multiplication algebraic methods.

Maths ppt linear equations in two variables

AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.

Linear equations in 2 variables

This document discusses linear equations. It defines linear equations as algebraic equations with terms that are constants or the product of constants and variables. Linear equations can have one or more variables. The document describes variables, constants, and examples of linear equations with one and two variables. It explains how to graph and solve systems of linear equations using graphical and algebraic methods like elimination and cross multiplication. Graphical methods involve plotting the lines defined by each equation and finding their point(s) of intersection. Algebraic methods eliminate variables to solve for the remaining ones.

Pairs of linear equation in two variable by asim rajiv shandilya 10th a

This document provides an overview of pairs of linear equations in two variables. It discusses representing such equations graphically as two lines with possible solutions of unique intersection, no intersection, or overlapping lines. Algebraic methods for solving pairs of linear equations are presented, including substitution, elimination of a variable by making coefficients equal, and cross multiplication. Examples are provided to illustrate each method. The document also describes how to reduce equations not initially in the standard form for a pair of linear equations to that form so the equations can be solved using the described algebraic techniques.

LINEAR EQUATION IN TWO VARIABLES PPT

The document provides information about solving linear equations and systems of linear equations. It defines a linear equation as an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses three methods for solving a pair of linear equations:
1) The graphical method involves plotting the equations on a graph and finding their point of intersection.
2) The algebraic methods include substitution, elimination, and cross-multiplication. Substitution involves solving one equation for one variable and substituting it into the other equation. Elimination involves eliminating one variable to obtain an equation with just one variable.
3) Cross-

Quadratic equations class 10

The document discusses quadratic equations. It defines the standard form of a quadratic equation as ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The values of x that satisfy the equation are called the roots. A quadratic equation can have two distinct real roots, two equal real roots, or no real roots depending on the discriminant. The quadratic formula x = (-b ± √(b2 - 4ac))/2a is presented to directly obtain the roots from the standard form. The discriminant (D = b2 - 4ac) determines the nature of the roots. If D > 0, there are two distinct real roots. If D = 0,

Pair of linear equations in two variables for classX

This document discusses methods for solving pairs of linear equations in two variables: substitution, elimination, and cross-multiplication. The substitution method involves solving one equation for one variable and substituting it into the other equation. The elimination method involves multiplying the equations by constants to make coefficients equal and then adding or subtracting the equations to eliminate one variable. The cross-multiplication method involves cross-multiplying the coefficients of the equations to derive an equation with one variable that can then be solved.

Linear equation in two variable

The document discusses methods for solving systems of linear equations in two variables:
1) Graphical method involves plotting the lines defined by each equation on a graph and finding their point of intersection.
2) Algebraic methods include substitution, elimination by equating coefficients, and cross-multiplication. Elimination involves manipulating the equations to eliminate one variable and solve for the other.
3) Examples demonstrate solving a system using substitution and elimination to find the solution values for x and y.

Pair Of Linear Equations In Two Variables

PowerPoint Presentation of Learning Outcomes, Experiential content, Explanation Content, Hot Spot, Curiosity Questions, Mind Map, Question Bank of
Pair Of Linear Equations In Two Variables Class X

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT

This document provides information about linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c. The document also discusses finding the solutions of linear equations, graphing linear equations, and equations of lines parallel to the x-axis and y-axis. Examples are provided to illustrate key concepts. In the summary, key points are restated such as linear equations having infinitely many solutions and the graph of a linear equation being a straight line.

PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10

THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .

Linear equations in two variables

This presentation include various methods of solving linear equations like substitution, elimination and cross-multiplication method.

PAIR OF LINEAR EQUATION IN TWO VARIABLE

Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
Friends if you found this helpful please click the like button. and share it :) thanks for watching

Pair of linear equations in 2 variables

This document provides information about solving pairs of linear equations in two variables. It discusses several methods for solving such equations, including elimination, substitution, and cross-multiplication. The elimination method involves multiplying equations by constants to eliminate one variable, then solving the resulting equation. The substitution method finds one variable in terms of the other from one equation, substitutes it into the other equation, and solves. Cross-multiplication uses the formula that the ratio of the coefficients of the variables in one equation equals the ratio of the constants. Word problems can also be solved by setting up linear equations from the information provided.

LINEAR EQUATION IN TWO VARIABLES

The document discusses linear equations in two variables. It provides examples of linear equations like x+y=176 and 2x+5=0. It states that a linear equation in two variables has infinitely many solutions, represented by an infinite set of x-y coordinate pairs that satisfy the equation. The graph of a linear equation in two variables is a straight line, where every point on the line is a solution to the equation.

Linear equtions with one variable

The document discusses equations and how to solve them. It defines an equation as a statement where two algebraic expressions are equal. It also defines a linear equation as one involving only one variable.
It then lists the four properties of equations: adding/subtracting the same quantity to both sides, multiplying/dividing both sides by the same quantity.
Next, it provides examples of how to solve different types of equations (those involving addition, subtraction, multiplication, or division of the variable) using both the traditional method of operations and the shortcut method of transposing terms.
Finally, it gives examples of solving equations with variables on both sides, word problems involving equations, and equations from applied contexts like age.

Linear equation in 2 variables

This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.

LINEAR EQUATION IN TWO VARIABLES

This document discusses linear equations and their properties and applications. It defines a linear equation as one where each term is either a constant or the product of a constant and two variables. Linear equations can be represented as ax + by + c = 0 and their graphs are straight lines. The solutions of a linear equation are the points that satisfy the equation. Linear equations are used to model many real-world situations where a change in input results in proportional change in output, such as doubling recipes, calculating grass growth rates, and budgeting money for various tasks. While useful for modeling within a "linear regime," systems often become nonlinear if inputs are increased too much.

Quadratic equation

1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.

PPT on Linear Equations in two variables

This ppt on different methods of solving equations like substitution method, elimination method, and cross multiplication method.

Coordinate geometry

Coordinate geometry describes the position of points on a plane using an ordered pair of numbers (x, y). It was developed by French mathematician René Descartes in the 1600s. The system uses two perpendicular axes (the x-axis and y-axis) that intersect at the origin point (0,0). Values to the right of the x-axis and above the y-axis are positive, while values to the left and below are negative. The plane is divided into four quadrants by these axes.

CLASS X MATHS Coordinate geometry

This document provides an overview of coordinate geometry. It defines key concepts like the Cartesian coordinate system, quadrants, and using an ordered pair (x,y) to locate points on a plane. It then explains how to calculate the distance between two points using the distance formula. Other topics covered include finding the area of a triangle using the coordinates of its vertices, using the section formula to divide a line segment internally, and finding the midpoint of two points.

Maths Project Quadratic Equations

This document provides information about quadratic equations, including:
- Methods for solving quadratic equations like factoring, completing the square, and using the quadratic formula.
- Key terms like discriminant and nature of roots. The discriminant determines if the roots are real, equal, or imaginary.
- Examples of solving quadratic equations using different methods and finding related values like discriminant and roots.

Quadratic Equation

This document introduces methods for solving quadratic equations beyond factoring, including the square root property, completing the square, and the quadratic formula. It discusses how to determine the number and type of solutions based on the discriminant. The key steps are presented for solving quadratics, graphing quadratic functions as parabolas, and finding the domain and range. Piecewise-defined quadratic functions are also explained.

polynomials of class 10th

This presentation discusses polynomials and their key properties. It defines what polynomials are, including their terms, degrees, and different types (constant, linear, quadratic, cubic). It explains the relationship between the zeros of a polynomial and its coefficients. Specifically, it states that the sum of the zeros is equal to the negative of the coefficient of x^1, and the product of the zeros is equal to the constant term. It also discusses how to find the zeros of a polynomial by setting it equal to 0 and factoring. Examples are provided to illustrate various polynomial concepts and properties.

Solving systems of linear equations by substitution

1) The substitution method for solving systems of linear equations involves solving one equation for one variable and substituting it into the second equation.
2) An example solves the system 2x + y = 4 and 3x + 2y = 7 by solving the first equation for y and substituting it into the second equation.
3) A system can have one solution, infinitely many solutions, or no solutions depending on whether the lines graph the same point, same line, or parallel lines.

Linear equations in two variables- By- Pragyan

This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.

Polynomials

This document summarizes key properties of polynomials, including that the sum of zeros is equal to the negative of the coefficient of x^2, and the product of zeros is equal to the negative of the constant term. It provides an example of finding the zeros of the polynomial x^2 + 7x + 12 and verifying these properties. It also gives an example of constructing a quadratic polynomial with given zeros of 4 and 1.

Mathematics ppt.pptx

1) The document provides information about linear equations in two variables including the general form of a linear equation, single linear equations, systems of two linear equations, conditions for common solutions, and methods to solve systems of linear equations algebraically.
2) Examples are provided to illustrate graphing single linear equations, finding common solutions to systems of two linear equations, and solving systems using elimination and cross-multiplication methods.
3) Key methods for solving systems of linear equations discussed include elimination by substitution or equating coefficients, and cross-multiplication. Conditions for common solutions depend on whether lines intersect, are parallel, or are coincident.

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

MATHS - Linear equation in two variable
(Class - X)
Maharashtra Board
Equations/Expressions
Word Problem

Pair Of Linear Equations In Two Variables

PowerPoint Presentation of Learning Outcomes, Experiential content, Explanation Content, Hot Spot, Curiosity Questions, Mind Map, Question Bank of
Pair Of Linear Equations In Two Variables Class X

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT

This document provides information about linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c. The document also discusses finding the solutions of linear equations, graphing linear equations, and equations of lines parallel to the x-axis and y-axis. Examples are provided to illustrate key concepts. In the summary, key points are restated such as linear equations having infinitely many solutions and the graph of a linear equation being a straight line.

PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10

THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .

Linear equations in two variables

This presentation include various methods of solving linear equations like substitution, elimination and cross-multiplication method.

PAIR OF LINEAR EQUATION IN TWO VARIABLE

Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
Friends if you found this helpful please click the like button. and share it :) thanks for watching

Pair of linear equations in 2 variables

This document provides information about solving pairs of linear equations in two variables. It discusses several methods for solving such equations, including elimination, substitution, and cross-multiplication. The elimination method involves multiplying equations by constants to eliminate one variable, then solving the resulting equation. The substitution method finds one variable in terms of the other from one equation, substitutes it into the other equation, and solves. Cross-multiplication uses the formula that the ratio of the coefficients of the variables in one equation equals the ratio of the constants. Word problems can also be solved by setting up linear equations from the information provided.

LINEAR EQUATION IN TWO VARIABLES

The document discusses linear equations in two variables. It provides examples of linear equations like x+y=176 and 2x+5=0. It states that a linear equation in two variables has infinitely many solutions, represented by an infinite set of x-y coordinate pairs that satisfy the equation. The graph of a linear equation in two variables is a straight line, where every point on the line is a solution to the equation.

Linear equtions with one variable

The document discusses equations and how to solve them. It defines an equation as a statement where two algebraic expressions are equal. It also defines a linear equation as one involving only one variable.
It then lists the four properties of equations: adding/subtracting the same quantity to both sides, multiplying/dividing both sides by the same quantity.
Next, it provides examples of how to solve different types of equations (those involving addition, subtraction, multiplication, or division of the variable) using both the traditional method of operations and the shortcut method of transposing terms.
Finally, it gives examples of solving equations with variables on both sides, word problems involving equations, and equations from applied contexts like age.

Linear equation in 2 variables

This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.

LINEAR EQUATION IN TWO VARIABLES

This document discusses linear equations and their properties and applications. It defines a linear equation as one where each term is either a constant or the product of a constant and two variables. Linear equations can be represented as ax + by + c = 0 and their graphs are straight lines. The solutions of a linear equation are the points that satisfy the equation. Linear equations are used to model many real-world situations where a change in input results in proportional change in output, such as doubling recipes, calculating grass growth rates, and budgeting money for various tasks. While useful for modeling within a "linear regime," systems often become nonlinear if inputs are increased too much.

Quadratic equation

1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.

PPT on Linear Equations in two variables

This ppt on different methods of solving equations like substitution method, elimination method, and cross multiplication method.

Coordinate geometry

Coordinate geometry describes the position of points on a plane using an ordered pair of numbers (x, y). It was developed by French mathematician René Descartes in the 1600s. The system uses two perpendicular axes (the x-axis and y-axis) that intersect at the origin point (0,0). Values to the right of the x-axis and above the y-axis are positive, while values to the left and below are negative. The plane is divided into four quadrants by these axes.

CLASS X MATHS Coordinate geometry

This document provides an overview of coordinate geometry. It defines key concepts like the Cartesian coordinate system, quadrants, and using an ordered pair (x,y) to locate points on a plane. It then explains how to calculate the distance between two points using the distance formula. Other topics covered include finding the area of a triangle using the coordinates of its vertices, using the section formula to divide a line segment internally, and finding the midpoint of two points.

Maths Project Quadratic Equations

This document provides information about quadratic equations, including:
- Methods for solving quadratic equations like factoring, completing the square, and using the quadratic formula.
- Key terms like discriminant and nature of roots. The discriminant determines if the roots are real, equal, or imaginary.
- Examples of solving quadratic equations using different methods and finding related values like discriminant and roots.

Quadratic Equation

This document introduces methods for solving quadratic equations beyond factoring, including the square root property, completing the square, and the quadratic formula. It discusses how to determine the number and type of solutions based on the discriminant. The key steps are presented for solving quadratics, graphing quadratic functions as parabolas, and finding the domain and range. Piecewise-defined quadratic functions are also explained.

polynomials of class 10th

This presentation discusses polynomials and their key properties. It defines what polynomials are, including their terms, degrees, and different types (constant, linear, quadratic, cubic). It explains the relationship between the zeros of a polynomial and its coefficients. Specifically, it states that the sum of the zeros is equal to the negative of the coefficient of x^1, and the product of the zeros is equal to the constant term. It also discusses how to find the zeros of a polynomial by setting it equal to 0 and factoring. Examples are provided to illustrate various polynomial concepts and properties.

Solving systems of linear equations by substitution

1) The substitution method for solving systems of linear equations involves solving one equation for one variable and substituting it into the second equation.
2) An example solves the system 2x + y = 4 and 3x + 2y = 7 by solving the first equation for y and substituting it into the second equation.
3) A system can have one solution, infinitely many solutions, or no solutions depending on whether the lines graph the same point, same line, or parallel lines.

Linear equations in two variables- By- Pragyan

This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.

Polynomials

This document summarizes key properties of polynomials, including that the sum of zeros is equal to the negative of the coefficient of x^2, and the product of zeros is equal to the negative of the constant term. It provides an example of finding the zeros of the polynomial x^2 + 7x + 12 and verifying these properties. It also gives an example of constructing a quadratic polynomial with given zeros of 4 and 1.

Pair Of Linear Equations In Two Variables

Pair Of Linear Equations In Two Variables

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT

PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10

PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10

Linear equations in two variables

Linear equations in two variables

PAIR OF LINEAR EQUATION IN TWO VARIABLE

PAIR OF LINEAR EQUATION IN TWO VARIABLE

Pair of linear equations in 2 variables

Pair of linear equations in 2 variables

LINEAR EQUATION IN TWO VARIABLES

LINEAR EQUATION IN TWO VARIABLES

Linear equtions with one variable

Linear equtions with one variable

Linear equation in 2 variables

Linear equation in 2 variables

LINEAR EQUATION IN TWO VARIABLES

LINEAR EQUATION IN TWO VARIABLES

Quadratic equation

Quadratic equation

PPT on Linear Equations in two variables

PPT on Linear Equations in two variables

Coordinate geometry

Coordinate geometry

CLASS X MATHS Coordinate geometry

CLASS X MATHS Coordinate geometry

Maths Project Quadratic Equations

Maths Project Quadratic Equations

Quadratic Equation

Quadratic Equation

polynomials of class 10th

polynomials of class 10th

Solving systems of linear equations by substitution

Solving systems of linear equations by substitution

Linear equations in two variables- By- Pragyan

Linear equations in two variables- By- Pragyan

Polynomials

Polynomials

Mathematics ppt.pptx

1) The document provides information about linear equations in two variables including the general form of a linear equation, single linear equations, systems of two linear equations, conditions for common solutions, and methods to solve systems of linear equations algebraically.
2) Examples are provided to illustrate graphing single linear equations, finding common solutions to systems of two linear equations, and solving systems using elimination and cross-multiplication methods.
3) Key methods for solving systems of linear equations discussed include elimination by substitution or equating coefficients, and cross-multiplication. Conditions for common solutions depend on whether lines intersect, are parallel, or are coincident.

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

MATHS - Linear equation in two variable
(Class - X)
Maharashtra Board
Equations/Expressions
Word Problem

Linear equations Class 10 by aryan kathuria

This document discusses linear equations and methods to solve systems of linear equations. It defines a linear equation as an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. Systems of linear equations can have unique solutions, infinite solutions, or no solutions depending on whether the lines intersect, are coincident, or are parallel. The document describes graphical and algebraic methods to solve systems, including elimination, substitution, and cross-multiplication methods. It provides examples of using each algebraic method to solve systems of two linear equations with two unknowns.

Linear equations in two variables

The document discusses linear equations in two variables. It defines linear equations as equations containing two variables where each variable has an exponent of 1. It provides examples and discusses the general form of simultaneous linear equations as a1x + b1y = c1 and a2x + b2y = c2. The document also discusses framing linear equations from word problems, graphically representing solutions, criteria for consistent/inconsistent systems, and methods for algebraically solving simultaneous linear equations including elimination, substitution, and cross multiplication.

Class 3.pdf

This document discusses solving simultaneous linear equations through algebraic and graphical methods. It covers:
- Algebraic methods like substitution and elimination to solve 2 equations with 2 unknowns.
- Graphing methods to find the point where two lines intersect, representing the solution.
- Conditions where equations have a unique solution, no solution, or infinitely many solutions.
- Extended examples are provided to demonstrate solving 2 and 3 equations with algebraic elimination.

Linear equations in two variables

Linear equations in two variables based on class 10th maths cbse
you can follow me on my insta manas.more12 for more ppts

linear equation in two variable.pptx

- The document discusses linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c.
- It describes how linear equations in two variables have infinitely many solutions, represented by pairs of x and y values. The graph of a linear equation in two variables is a straight line.
- The document also discusses how equations of lines parallel to the x-axis or y-axis can be represented. The graph of an equation of the form x = a is a line parallel to the y-axis, while an equation of the form y = a graphs as a line parallel to the x-axis.

Lecture 11 systems of nonlinear equations

The document discusses solving systems of nonlinear equations in two variables. It provides examples of nonlinear systems that contain equations that are not in the form Ax + By = C, such as x^2 = 2y + 10. Methods for solving nonlinear systems include substitution and addition. The substitution method involves solving one equation for one variable and substituting into the other equation. The addition method involves rewriting the equations and adding them to eliminate variables. Examples demonstrate both methods and finding the solution set that satisfies both equations.

C2 st lecture 2 handout

This document provides a summary of lecture 2 on quadratic equations and straight lines. It covers how to factorize, complete the square, and use the quadratic formula to solve quadratic equations. It also discusses how to find the equation of a straight line given its gradient and y-intercept, or two points on the line. Additionally, it explains how to sketch lines, find the midpoint and distance between two points. Key terms defined include quadratic, surd, gradient, and intercept. Methods demonstrated include solving quadratic equations, finding lines from gradient/point and two points, and calculating midpoints and distances on a graph.

Pair of linear equation in two variables

it has all the discription about the easy chapter pair of linear equation in two variables. and if you like it so pleras

TABREZ KHAN.ppt

The document is a maths project report for class 12th student Tabrez Khan on the topic of determinants. It contains definitions and properties of determinants of order 1, 2 and 3 matrices. It discusses minors, cofactors and applications of determinants like solving systems of linear equations using Cramer's rule. It also contains examples of evaluating determinants and applying properties of determinants to simplify expressions.

Analytic Geometry Period 1

The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.

Topic 8 (Writing Equations Of A Straight Lines)

The document provides information on properties of straight lines and methods to write equations of straight lines given different conditions. It also discusses solving systems of linear equations using different methods like graphing, substitution, elimination and Cramer's rule. Key points covered include writing equations in slope-intercept and standard form, finding slopes of parallel and perpendicular lines, and properties of consistent, inconsistent and dependent systems of linear equations.

Aieee Maths 2004

This document contains 60 multiple choice questions from a past mathematics exam. The questions cover a range of topics including relations, functions, complex numbers, matrices, determinants, quadratic equations, arithmetic and geometric progressions, binomial expansions, trigonometry, calculus, differential equations, vectors, conic sections, and three-dimensional geometry. For each question, four choices are given and the student must select the correct answer.

Algebra

The document discusses solving simultaneous linear equations using the substitution method. It begins by explaining how to reduce a set of simultaneous linear equations into a single linear equation with one unknown. This is done by substituting one equation into the other to eliminate one of the unknowns. Three examples are then worked through step-by-step to demonstrate the substitution method. The key steps are: 1) express one unknown in terms of the other, 2) substitute this into the other equation to get a single-variable equation, 3) solve for the value of the unknown, and 4) back-substitute to find the value of the other unknown. Checking the solution involves substituting the values back into the original equations.

Persamaan fungsi linier

This document discusses linear functions and systems of linear equations. It begins by defining the standard form of a linear function as y = mx + b, where m is the slope and b is the y-intercept. It then discusses various ways to determine the equation of a linear function given different inputs like slope and a point, or two points. The document also discusses how to graph linear functions and systems of linear equations. It describes three possible solutions for a system of two equations with two unknowns: a unique solution, no solution, or infinitely many solutions. Finally, it covers two methods for solving systems of linear equations: elimination and substitution.

Linear equations

The document discusses various methods for solving systems of simultaneous linear equations with two variables. It explains that a system contains two or more linear equations involving the same variables. Common methods covered include substitution, where one variable is solved for and substituted into the other equation, and elimination, where coefficients are multiplied and equations are combined to eliminate one variable. Examples are provided to demonstrate both methods step-by-step. It emphasizes that solutions found must satisfy both original equations.

Linear equations in Two Variable

The document discusses systems of linear equations and methods for solving them. It defines a system of linear equations as a pair of linear equations in two variables. It presents two examples of systems of linear equations. It then describes algebraic methods for solving systems, including elimination by substitution, elimination by equating coefficients, and cross multiplication. It provides examples of using elimination by substitution and elimination by equating coefficients to solve systems of two equations with two unknowns.

Pair of linear equations in two variable

Order of presentation
Anushka - Opening
Nikunj -Intro
Shubham - Graphical
Amel - Sunstitution
Siddhartha- Elimination
Karthik - Cross multiplication
Anushka - Equations reducible...& wrap-up
In case of any confusion..inform me by facebook, phone or in school

Sect5 1

This document introduces concepts related to second-order linear differential equations including superposition of solutions, existence and uniqueness of solutions, linear independence, the Wronskian, and general solutions. It provides 16 examples of imposing initial conditions on general solutions to obtain particular solutions. It also includes problems assessing understanding of related concepts and solving characteristic equations.

Mathematics ppt.pptx

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Analytic Geometry Period 1

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CLASS IV ENGLISH

This document provides examples of compound words formed by joining two words together, such as "rainbow", "butterfly", and "snowman". It then asks the reader to identify compound words in sentences and lists of words. Examples of compound words given include "camper", "doghouse", and "lighthouse". The document concludes by asking the reader to create their own compound words by joining two words.

CLASS 4 MATHS

This document contains 15 multiple choice questions about volumes of liquids measured in milliliters and liters. It is a quiz about common volumes like a teaspoon, a mug of tea, and the gas tanks of cars, as well as larger volumes like swimming pools. Players earn hypothetical cash prizes for answering the questions correctly, with the potential to win 1 million rupees for answering the final question about the volume of an Olympic swimming pool.

CLASS 4 MATHS

The document discusses a class trip to Bhopal where 210 children from grades 1-5 will attend. It calculates that 4 regular buses, each able to hold 50 children, would be needed for transportation. However, the buses available are mini buses that can only hold 35 children each. So the document prompts calculating how many mini buses would be required to transport all 210 children.

CLASS III MATHS

This document discusses different views of objects and symmetry. It contains pictures of objects with their front, back, top, and side views labeled. It also contains pictures that are divided in half along a dotted line and asks students to draw the other half using a mirror. The document suggests activities for students like making shapes with dots, listing symmetrical letters, and identifying which objects can be divided into equal halves with a dotted line. It includes two worksheets with questions about views of objects and drawing lines of symmetry.

CLASS III MATHS

The document lists comparative adjective pairs in three categories: longer-shorter, tallest-shortest, thickest-thinnest. It repeats the pairs "taller-shorter" and "tallest-shortest" multiple times and also includes the pairs "longest-shortest", "heavier-lighter", and "heaviest-lightest".

Changing times.

Chetandas describes his life experiences moving from India to Pakistan as a child after the countries divided. He helped his parents build their first home using local materials like mud, husk, cow dung and wood. Over the years he got married, had children, and built additional rooms. His children are now grown and he is planning to build a new home with modern materials like bricks, cement and running water. Chetandas has seen many changes over his lifetime in how homes are constructed.

3 class english

This document describes different sounds that can be heard on the road, including birds singing, cycles ringing their bells, vegetable sellers calling out what they are selling, school children chatting, and the tramping sound of shoes on the pavement. It also identifies common birds like crows that caw in the mornings and sparrows that chirp. Rules for walking and crossing roads safely are provided, along with values around road safety like prioritizing safety over speed.

Clss ii english-the mouse---

A mouse found a pencil and started chewing on it. The pencil pleaded with the mouse, saying "You are hurting me," and asked if it could draw one last picture before the mouse continued chewing. The pencil hoped its request would make the mouse stop chewing and potentially harming it.

Rainbow

The document discusses various topics including the brightness of the sun, favorite fruits, plants in gardens, fruits lying outside baskets, and colors like yellow, orange, blue, red, violet, green and indigo. It also includes short phrases about inside and outside, awake and asleep, love and hate, and an activity to match opposite words.

NUMBERS 1 TO 20

This document lists the numbers from 10 to 20 in ascending order, with each number on its own line. It provides a simple listing of the integers from 10 through 20 without additional context or explanation.

TIME

This document outlines a student's daily schedule and asks questions about the timing of activities. It describes the student waking up in the morning, eating breakfast, going to school, having lunch, playing, studying, and going to bed. It then asks which activities take place in the morning, evening, day, and night and which activity takes the longest time.

MEASUREMENTS

This document contains questions about comparing the length, height, weight, and other attributes of different objects. It asks which object is longer/shorter, tallest/shortest, heavier/lighter, and which house and tree have specific attributes. The questions are assessing skills in comparing attributes and determining which object has a superlative quality like being the longest, tallest or heaviest.

DATA HANDLING

Sudha and her sister Harini want to separate and count the fruits in a basket their father brought for a family pooja. They counted 6 bananas, 3 apples, 5 oranges, 2 grapes, and 8 mangoes. The document provides worksheets and questions to help students practice organizing and analyzing data.

Who is heavier

The document is a story about a boy named Shiva learning about what makes objects heavier or lighter from his grandfather. His grandfather has him hold different objects like a sharpener, book, lock, and crayon to understand which feels heavier. Through this interactive lesson, Shiva learns that heavier objects are harder to carry than lighter objects. His grandfather reinforces this by having Shiva watch a video and answer questions correctly about which common items are heavier or lighter.

The tiger and the mosquitoe

A tiger was napping under a tree when an annoying mosquito started buzzing around him. When the tiger tried to swat the mosquito away with his paws, he ended up hitting himself both times and scraping his cheek, making it bleed. Unable to hit the evasive mosquito, the embarrassed tiger walked away as the mosquito called out that everyone has their strengths.

Photoshop

Photoshop is image editing software created by Thomas Knoll in 1987. It contains various tools for selection, painting, and editing images organized in a toolbar. Key tools include selection tools like the marquee and lasso tools, painting and editing tools like the brush and crop tools, and tools to work with layers and colors. Photoshop allows users to open, edit, and save images in various formats like PSD, JPEG, and TIFF. Images can be created or modified using layers, tools, and options like adding text.

COMPUTERS Database

This document provides an overview of databases and database management systems (DBMS). It discusses what a database is, components of a database system like users and applications, and examples of DBMS like MySQL and Oracle. It also summarizes key database concepts such as data models, relationships between data using keys, and relational algebra operations for querying databases.

Dove

Dove

CLASS IV ENGLISH

CLASS IV ENGLISH

CLASS 4 MATHS

CLASS 4 MATHS

CLASS 4 MATHS

CLASS 4 MATHS

CLASS III MATHS

CLASS III MATHS

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3 class english

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Clss ii english-the mouse---

Clss ii english-the mouse---

Rainbow

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NUMBERS 1 TO 20

NUMBERS 1 TO 20

TIME

TIME

MEASUREMENTS

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DATA HANDLING

DATA HANDLING

patterns

patterns

Who is heavier

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Sundari

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The tiger and the mosquitoe

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Photoshop

Photoshop

COMPUTERS Database

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Pharmaceutics Pharmaceuticals best of brub

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ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
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2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
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3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
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- 1. LINEAR EQUATIONS IN TWO VARIABLES
- 2. INTRODUCTION General Form of Linear Equation in Two Variables a x + b y +c = 0, a ≠ 0, b ≠ 0, a, b, c are real numbers Solution Values of x and y, for given a, b, c, such that a x + b y +c = 0
- 3. Single linear equation Example 3 x – 2 y + 4 = 0 (1) Infinitely many values of x and y satisfy equation (1) x -3 -2 -1 0 1 2 3 4 5 y -2.5 -1 0.5 2 3.5 5 6.5 8.0 9.5 •All (x, y) values satisfying equation (1) lie on a straight line – (0, 2) satisfies equation (1) and lies on straight line • Graph of the equation (1) is shown in Figure 1 Figure 1
- 4. Single linear equation • Every day example : Cost of two oranges is Rs. 4 more than the cost of 3 bananas • Assume cost of a banana is x Rs. and cost of an orange is y Rs., then the relationship between cost of bananas and oranges is given by 2 y = 3 x + 4 (1) • The graph of equation (1) is the straight line in Figure 1 • Many similar relationships can be expressed by a linear algebraic equation in two variables. • Geometrically a linear equation in two variables can be represented by a straight line in the Cartesian Plane.
- 5. Single linear equation • Adding and subtracting a number on both sides of the equation does not change the equation 3 x –2 y + 4 +(10) = 0 + (10) • Multiplying or dividing both sides of the equation does not change the equation 2*(3 x –2 y + 4) = 3 x – 2 y + 4 = 0
- 6. System of two linear equations Two linear equations in x and y 3 x – 2 y + 4 = 0 (1) x + 2 y + 4 = 0 (2) Graph of the two linear equations Figure 2
- 7. System of two linear equations • Both the linear equations are straight lines • The two straight lines intersect at (-2 ,-1) x = -2, y = -1 satisfy both the equations 3 x - 2 y + 4 = 3 *(-2) – 2* (-1) + 4 = 0 x + 2 y +4 = (-2) + 2* (-1) + 4 = 0 • (-2 , -1 ) is a common solution of the two linear equations
- 8. Condition for common solution Consider two linear equations 2 x + 3 y = 6 (1) 4 x + 6 y = 24 (2) • Both lines are parallel and do not intersect • No common solution if lines are parallel Figure 3 Graph of equation (1) and equation (2) in Figure 3
- 9. Condition for common solution (Contd.) Consider another two linear equations x + y = 3 (1) 7 x + 7 y = 21 (2) Figure 4 Graph of equation (1) and equation (2) in Figure 4 • Both straight lines are parallel • They are also same or coincident •Only one straight line and hence infinitely many solutions
- 10. Condition for common solution (Contd.) Two linear equations represented by two straight lines can 1. Have a unique common solution if the two straight lines intersect. 2. Have no common solution if the two straight lines are parallel. 3. Have infinitely many solutions if the two straight lines are same or coincident.
- 11. Algebraic Solution of System of Linear Equations • Method of Elimination by Substitution Consider two linear equations 2 x – y = 3 (1) 4 x – y = 5 (2) 1. Solve for y from equation (1) pretending x to be a constant, we get y = 2 x – 3 (3) 2. Substitute y from (3) to (2) to get 4 x – (2 x –3) = 5 (4) y is eliminated in Step 2. and we can now solve for x from (4) 2 x + 3 = 5 => x = 1 3. Substitute x = 1 in (1), to get 2 – y = 3 => y = – 1 (1, – 1) satisfy equations (1) and (2). Hence the solution is correct.
- 12. Algebraic Solution of System of Linear Equations (Contd.) • Method of Elimination by Equating Coefficients Consider two linear equations 11 x – 5 y + 61 = 0 (1) 3 x – 20 y – 2 = 0 (2) 1. Multiply equation (1) by 3 and equation (2) by 11 to get 33 x – 15 y + 183 = 0 (3) 33 x – 220 y – 22 = 0 (4) 2. Subtract (4) from (3) to get 205 y + 205 = 0 or y = – 1 3. Substitute y = – 1 in (2), we get 3 x – 20 *(– 1) – 2 = 0 or 3 x = – 18 or x = – 6 (-6, -1) satisfies (1) and (2) and hence is a correct solution.
- 13. Solution of System of Linear Equations by Cross Multiplication Consider two linear equations a1 x + b1y + c1 = 0, a1≠ 0, b1≠ 0 (1) a2 x + b2 y + c2 = 0, a2 ≠ 0, b2 ≠ 0 (2) Eliminate y by substitution. From (1) we get y = – (1/ b1 )(c1 + a1 x) b1 ≠ 0 (given) Substitute y in (2), we get a2 x + b2 [– (1/ b1 )(c1 + a1 x) ] + c2 = 0 or (a1 b2 - a2 b1 ) x = b1 c2 - b2 c1 (3) Similarly by eliminating x, we get (a1 b2 - a2 b1 ) y = c1 a2 - c2 a1 (4)
- 14. Solution of System of Linear Equations by Cross Multiplication • Case 1: (a1 b2 – a2 b1) ≠ 0 x = (b1 c2 – b2 c1)/(a1 b2 - a2 b1) y = (c1 a2 – c2 a1)/(a1 b2 - a2 b1) The above can be written as __ x_______ = __ y_______ = __ 1_______ b1 c2 – b2 c1 c1 a2 – c2 a1 a1 a1 b2 - a2 b1
- 15. Solution of System of Linear Equations by Cross Multiplication • Case 2 : (a1 b2 – a2 b1) = 0 In this case we can not divide by a1 b2 – a2 b1 to get x and y For a1 b2 – a2 b1 = 0, we get a1 = k a2 and b1= k b2 • c1 = k c2then equation (1) becomes k a2 x + k b2 y + k c2 = 0 or k (a2 x + b2 y + c2) = 0 or a2 x + b2 y + c2 = 0 Hence equation (1) and (2) are same and there are infinitely many solutions
- 16. Solution of System of Linear Equations by Cross Multiplication • c1 ≠ k c2 then equation (1) becomes or k (a2 x + b2 y) + c1= 0 or k (- c2) + c1= 0 or c1= k c2 k a2 x + k b2 y + c1 = 0 which is not true. Hence, no solution exists.
- 17. Example Problems • 1) Solve by eliminating y : x+y=7; 2x–y=5 • Solution: x+y=7 (1) 2x-y=5 (2) (1)+(2) => x = 4 • Substituting x value in (1) 4+y =7 => y = 3
- 18. Example Problems • 2) Solve by eliminating coefficients: x+y = a+b; ax-by =a2 -b2 • Solution: x+y = a+b (1) ax-by = a2 -b2 (2) • Multiplying (1) by b, we get bx+by = ab +b2 (1) + (2) => x(a + b) = a(a+b) x = a and y = b
- 19. Example Problems 3) Solve by cross multiplication: x+y=17; 12x-5y =17 • Solution: x+y=17 x+y-17=0 12x-5y=17 12x-5y-17=0 x y 1 1 -17 1 1 -5 -17 12 -5 •By cross-multiplication rule, we get x = 6 and y= 11
- 20. THANK YOU